Mines' End lies at the bottom of the Gnomish Mines. It will be either the 8th or 9th level of that branch and will therefore occur somewhere between Dlvl10 and Dlvl13. There are three versions of Mines' End; each of which is guaranteed to contain a luckstone.

A notable fact is that Mines' End, being the lowest level of the Gnomish Mines, has undiggable floor. Therefore, zapping a wand of digging downwards—one of several ways of escaping looming death—will have not quite the desired effect.

Credit for all maps in this article goes to the NetHack Gazetteer's Mines' End page.

The Mimic of the Mines

This level contains seven hidden places, marked on the map below. Six of them are behind secret doors, and the seventh is behind a narrow choke point. One of these hidden places contains a luckstone, another contains a loadstone, four contain mimics pretending to be gray stones, and one is empty. In addition, there are two random tools, seven random gems, and three other random objects placed throughout the level. The walls are undiggable.

The Gnome King's Wine Cellar

This version contains six guaranteed potions of booze (as the name would suggest) in stacks of two, with some 3rd potion. The bottom stack is guaranteed to have a potion of object detection; the others are random. There are two random tools, seven random gems, three other random objects, and six random traps scattered throughout the level. The luckstone is at the chamber in the far right; the blank tiles are rock that needs to be dug out to reach this chamber. The chamber also contains one ruby and one emerald (SW), two diamonds (NW), two emeralds (NE), two amethysts, one ruby and one luckstone (SE), as well as a few random gems. To get to the hidden gem cache, you can teleport in or dig with a pickaxe. As the spell/wand of digging only digs one tile here, you'll need more charges than one wand can hold, so they make a poor choice.

Nethack 3.6 changed this map slightly, and now has some randomness to it.
Tiles with a H might be walls or floor. The tile with D will contain a (locked) Secret door in case the entrance at the lower right is walled off.
Some of these walls are mutually exclusive so that there will always be a way to reach every part of the level without digging. For details check Source:NetHack 3.6.0/dat/mines.des#line983.

The Catacombs

This level is unmappable and contains a randomly-generated maze. The level walls, the large chambers, and the possible locations of the luckstone are fixed. There are three possible locations for the luckstone. The two locations that do not contain the luckstone will have nothing and a flint stone respectively. The luckstone and flint stone lie on a level teleporter. The rest of the level contains two diamonds, three emeralds, two rubies, two amethysts, seven other random gems, five random scrolls, four random spellbooks, three other random objects, and seven more random traps (so that the chance of at least one polytrap is 55.6%).[1] The spellbooks and scrolls make this the most desirable level for spellcasters, but it is also the most difficult, because the starting room often contains several powerful monsters in a small space. There are two random V in the level, and there may well be a minotaur hiding out in the maze. Stay on the up stairs, and don't forget Elbereth (although be aware that it will not work on the minotaur - in most cases you are better off going up and coming back when you are strong enough to face it).

The dotted areas are always open floor; the < is the upstairs; the *s mark the locations of the luck and flint stones; and the { are fountains. The rest of the level is filled with random maze.

SLASH'EM

SLASH'EM contains an additional level to the Gnomish Mines which is reached by a down staircase in the now misnamed Mines' End. The Mine King level can also be dug to through the floor of Mines' End. This is important mainly not as an escape, but as a warning to be alert for trapdoors which can drop you into a situation you are not prepared for (the new final level of the mines can be difficult for the unprepared). The down staircase will be located on one of the possible luckstone locations for the "Mimic of the Mines" and the "Catacombs" variants and immediately next to the gem cache in the "Gnome King's Wine Cellar" variant.